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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the ideal structure of Banach algebras


Author: William E. Dietrich
Journal: Trans. Amer. Math. Soc. 169 (1972), 59-74
MSC: Primary 46J20; Secondary 43A20, 46J10
MathSciNet review: 0308791
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Abstract: For Banach algebras $ A$ in a class which includes all group and function algebras, we show that the family of ideals of $ A$ with the same hull is typically quite large, containing ascending and descending chains of arbitrary length through any ideal in the family, and that typically a closed ideal of $ A$ whose hull meets the Šilov boundary of $ A$ cannot be countably generated algebraically.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0308791-2
PII: S 0002-9947(1972)0308791-2
Keywords: Zero set, approximate identity, chains of ideals, countably generated, closed ideals in a Banach algebra
Article copyright: © Copyright 1972 American Mathematical Society